<p><b>Abstract</b>—The objective of solid modeling is to represent, manipulate, and reason about, the three-dimensional shape of solid physical objects, by computer. Such representations should be unambiguous.</p><p>Solid modeling is an application-oriented field that began in earnest in the early 1970s. [<ref rid="bibv000346" type="bib">46</ref>]. Major application areas include design, manufacturing, computer vision, graphics, and virtual reality. Technically, the field draws on diverse sources including numerical analysis, symbolic algebraic computation, approximation theory, applied mathematics, point set topology, algebraic geometry, computational geometry, and data bases. Monographs and major surveys of solid modeling include [<ref rid="bibv000313" type="bib">13</ref>], [<ref rid="bibv000319" type="bib">19</ref>], [<ref rid="bibv000327" type="bib">27</ref>], [<ref rid="bibv000337" type="bib">37</ref>], [<ref rid="bibv000344" type="bib">44</ref>], [<ref rid="bibv000345" type="bib">45</ref>], [<ref rid="bibv000346" type="bib">46</ref>].</p><p>In this road map article, we begin with some mathematical foundations of the field. We review next the major representation schemata of solids. Then, major layers of abstraction in a typical solid modeling system are characterized: The lowest level of abstraction comprises a substratum of basic service algorithms. At an intermediate level of abstraction there are algorithms for larger, more conceptual operations. Finally, a yet higher level of abstraction presents to the user a functional view that is typically targeted towards solid design. Here, we will look at some applications and at user interaction concepts.</p><p>The classical design paradigms of Solid Modeling concentrated on obtaining one specific final shape. Those paradigms are becoming supplanted by feature-based, constraint-based design paradigms that are oriented more toward the design process and define classes of shape instances. These new paradigms venture into territory that has yet to be explored systematically. Concurrent with this paradigm shift, there is also a shift in the system architecture towards modularized confederations of plug-compatible functional components. We explore these trends lightly in the last section.</p>